Mathematical Characterization of Signal Semantics and Rethinking of the Mathematical Theory of Information

Shannon information theory is established based on probability and bits, and the communication technology based on this theory realizes the information age. The original goal of Shannon's information theory is to describe and transmit information content. However, due to information is related to cognition, and cognition is considered to be subjective, Shannon information theory is to describe and transmit information-bearing signals. With the development of the information age to the intelligent age, the traditional signal-oriented processing needs to be upgraded to content-oriented processing. For example, chat generative pre-trained transformer (ChatGPT) has initially realized the content processing capability based on massive data. For many years, researchers have been searching for the answer to what the information content in the signal is, because only when the information content is mathematically and accurately described can information-based machines be truly intelligent. This paper starts from rethinking the essence of the basic concepts of the information, such as semantics, meaning, information and knowledge, presents the mathematical characterization of the information content, investigate the relationship between them, studies the transformation from Shannon's signal information theory to semantic information theory, and therefore proposes a content-oriented semantic communication framework. Furthermore, we propose semantic decomposition and composition scheme to achieve conversion between complex and simple semantics. Finally, we verify the proposed characterization of information-related concepts by implementing evolvable knowledge-based semantic recognition.